To find the absolute-value equation for the given points (2,1), (3,2), (4,3), (2,1), (1,2), (0,3), (-1,4), (-2,5), observed symmetry around y = x + 1. The correct equation is y = |x - 2| + 1.
1. Initial Observation:
- Observe symmetry around the line y = x + 1, suggesting an absolute-value difference, |y - (x + 1)|.
2. Formulating an Initial Equation:
- Initially consider y = |y - (x + 1)|.
3. Refinement based on Observations:
- Notice that the distance should be from x = 2, not x = -1.
- Rewrite as y = |x + 1 - 2| + 1.
4. Verification with Given Points:
- Check if the equation y = |x - 2| + 1 fits the given points.
- For (2, 1): |1 - 2| + 1 = 2
- For (3, 2): |2 - 2| + 1 = 2
- ... and so on.
5. Final Confirmation:
- Confirm that the equation y = |x - 2| + 1 matches all given points, validating its correctness.